(Uncorrected OCR)
Abstract
A prediction of Black-Scholes (1973) formula is that all option prices on the same underlying security with the same expiration but with different exercise prices should have the same implied volatility. But in practice, when the Black-Scholes formula is inverted to imply volatilities from reported option prices, the volatility estimates seem to be different across exercise prices.
This thesis examines empirically the smile behavior in Hang Seng Index (HSI) options market in Hong Kong. HSI options market is characterized by experiencing two types of trading systems: open out-cry trading system and electronic trading system. In terms of the efficiency of price and trade reporting, these two trading systems are quite different. The first objective of this research is to analyze the factors explaining the volatility smile for two consecutive subperiods with different market structure and to contrast the determinants of the implied volatility function for the two subperiods. The empirical results indicate that the implied volatilities for Hang Seng Index options tend to smile consistently through the whole sample period. When explaining the variability of the implied volatility function, the volatility of the underlying asset and time to expiration seem to be key variables in both subperiods. However the transaction costs proxied by the effective bid-ask spread appear to affect the curvature of the volatility function only in the subperiod that employs screen-based trading system.
My second part of study is motivated by a special practice employed by HSI options market. According to this practice, a piecewise linear volatility function was adopted by HSI options market for the settlement purpose. That is, the settlement is made based on a daily piecewise linear ?mile?or ?mirk?volatility function that is set by market-makers and not directly by market forces. To investigate to what extent this artificial pattern is the same as the one driven by the market forces, I estimate a market-determined piecewise linear volatility function and analyze the relationship between the determinants of the parameters provided by
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market-makers with those estimated from market trading information. The results indicate that the linear implied volatility function could be a good substitute of the quadratic function in Hong Kong when using in practice. The factors that are key determinants of the curvature of the volatility smile in quadratic function are all important factors to influence the slope of the linear function. By comparing the volatility function set up by market makers with one estimated using actual trading data, I may conclude that although the differences between pairs of function parameters are significant, HSI options market makers do have a comprehensive consideration when they set up the volatility function parameters.
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